Rewrite as a simplified fraction. ${0.50\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 504.4444...\\ 100x &= 50.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 454}$ ${x = \dfrac{454}{900}} $ ${x = \dfrac{227}{450}} $